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A histogram is titled 'Exam Scores per Student in Mr. Hanley's Class.' The x-axis ranges from 40 to 100 by 10-unit increments and the y-axis ranges from 0 to 8 by 2-unit increments. The x-axis is labeled 'Exam Scores' and the y-axis is unlabeled.

A histogram is titled 'Exam Scores per Student in Ms. Blach's Class.' The x-axis ranges from 40 to 100 by 10-unit increments and the y-axis ranges from 0 to 5 by increments of 1. The x-axis is labeled 'Exam Scores' and the y-axis is unlabeled.
Mr. Hanley and Ms. Balch gave the same Algebra final exam to their classes. The histograms show the distribution of the scores for each class. One of the classes will get extra tutoring following the exam to help them with the topics they missed on the exam. Which class likely needs more tutoring help, and why?

(1 point)
Responses

Ms. Balch’s class needs the tutoring because the class data is skewed right, and her class median is lower.
Ms. Balch’s class needs the tutoring because the class data is skewed right, and her class median is lower.

Mr. Hanley’s class needs the tutoring because the class data is skewed left, and his class median is higher.
Mr. Hanley’s class needs the tutoring because the class data is skewed left, and his class median is higher.

Mr. Hanley’s class needs the tutoring because the class data is skewed right and his class median is lower.
Mr. Hanley’s class needs the tutoring because the class data is skewed right and his class median is lower.

Ms. Balch’s class needs the tutoring because the class data is skewed left and her class median is higher.
Ms. Balch’s class needs the tutoring because the class data is skewed left and her class median is higher.
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1 answer

To determine which class likely needs more tutoring help, we should analyze the histograms based on their shapes and distributions (skewness) as well as the potential medians.

  1. Histogram of Mr. Hanley's Class:

    • The y-axis data ranges from 0 to 8 and appears to indicate a wider spread of scores, potentially with a concentration towards one side.
    • If the class has scores heavily towards the higher end (80-100), it suggests a left skew (more scores on the higher end and fewer on the lower end). If there’s a concentration of scores low (40-60) with fewer high scores (80-100), it could indicate the opposite.

  2. Histogram of Ms. Balch's Class:

    • The y-axis here ranges from 0 to 5, potentially showing a lower frequency of higher scores.
    • Depending on its shape, if more scores are on the lower end (40-60) and fewer higher ones (80-100), it suggests a right skew.

With these insights in mind, let’s evaluate the responses:

  • Ms. Balch’s class needs the tutoring because the class data is skewed right, and her class median is lower — This option implies that the overall performance is poorer, as a right-skewed distribution would mean a significant number of students scored lower.

  • Mr. Hanley’s class needs the tutoring because the class data is skewed left, and his class median is higher — If the data are skewed left, while the median is higher, this suggests that most students did well, indicating lower tutoring needs.

  • Mr. Hanley’s class needs the tutoring because the class data is skewed right and his class median is lower — This contradicts the premise of a well-performing class.

  • Ms. Balch’s class needs the tutoring because the class data is skewed left and her class median is higher — If her class data were indeed skewed left, it would generally indicate higher performance.

Based on this analysis, the best choice is:

Ms. Balch's class needs the tutoring because the class data is skewed right, and her class median is lower.

This option suggests that her class overall performed worse on the exam, indicating a greater need for tutoring assistance.